Date & Time: 19th March 2017, 12:30 pm

Duration: 3h

If a line makes angles 90° and 60° respectively with the positive directions of *x* and *y* axes, find the angle which it makes with the positive direction of *z*-axis.

Chapter: [0.02] Inverse Trigonometric Functions

Evaluate : `int_2^3 3^x dx`

Chapter: [0.07] Integrals

Determine the value of the constant 'k' so that function f(x) `{((kx)/|x|, ","if x < 0),(3"," , if x >= 0):}` is continuous at x = 0

Chapter: [0.05] Continuity and Differentiability

If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A^{–1}) = (det A)^{k}

Chapter: [0.03] Matrices

Chapter: [0.13] Probability

A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs 100 and that on a bracelet is Rs 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit?

It is being given that at least one of each must be produced.

Chapter: [0.12] Linear Programming

Find `int dx/(x^2 + 4x + 8)`

Chapter: [0.07] Integrals

Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z.

Chapter: [0.1] Vectors

Show that the function f(x) = 4x^{3} - 18x^{2} + 27x - 7 is always increasing on R.

Chapter: [0.06] Applications of Derivatives

The volume of a sphere is increasing at the rate of 3 cubic centimeter per second. Find the rate of increase of its surface area, when the radius is 2 cm

Chapter: [0.06] Applications of Derivatives

Show that all the diagonal elements of a skew symmetric matrix are zero.

Chapter: [0.03] Matrices

if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`

Chapter: [0.09] Differential Equations

Let `veca = hati + hatj + hatk = hati` and `vecc = c_1veci + c_2hatj + c_3hatk` then

1) Let `c_1 = 1` and `c_2 = 2`, find `c_3` which makes `veca, vecb "and" vecc`coplanar

2) if `c_2 = -1` and `c_3 = 1`, show that no value of `c_1`can make `veca, vecb and vecc` coplanar

Chapter: [0.1] Vectors

If `veca, vecb, vecc` are mutually perpendicular vectors of equal magnitudes, show that the vector `veca + vecb+ vecc` is equally inclined to `veca, vecb` and `vecc`.

Chapter: [0.1] Vectors

If `veca, vecb, vecc` are mutually perpendicular vectors of equal magnitudes, find the angle which `veca + vecb + vecc`make with `veca or vecb or vecc`

Chapter: [0.1] Vectors

The random variable X can take only the values 0, 1, 2, 3. Give that P(X = 0) = P(X = 1) = p and P(X = 2) = P(X = 3) such that `Sigmap_i x_i^2 = 2Sigmap_ix_i`. Find the value of p

Chapter: [0.13] Probability

Often it is taken that a truthful person commands, more respect in the society. A man is known to speak the truth 4 out of 5 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

Do you also agree that the value of truthfulness leads to more respect in the society?

Chapter: [0.13] Probability

Using properties of determinants, prove that `|(x,x+y,x+2y),(x+2y, x,x+y),(x+y, x+2y, x)| = 9y^2(x + y)`

Chapter: [0.04] Determinants

Let A = `((2,-1),(3,4))`, B = `((5,2),(7,4))`, C= `((2,5),(3,8))` find a matrix D such that CD − AB = O

Chapter: [0.03] Matrices

Differentiate the function with respect to *x*.

`(sin x)^x + sin^(-1) sqrtx`

Chapter: [0.05] Continuity and Differentiability

if `x^m y^n = (x + y)^(m + n)`, prove that `(d^2y)/(dx^2)= 0`

Chapter: [0.05] Continuity and Differentiability

Evaluate `int_0^pi (x sin x)/(1 + cos^2 x) dx`

Chapter: [0.07] Integrals

Evaluate `int_0^(3/2) |x sin pix|dx`

Chapter: [0.07] Integrals

Solve the following L.P.P graphically: Maximise Z = 20*x** *+ 10*y*

Subject to the following constraints x + 2y ≤ 28,

3x + y ≤ 24,

x ≥ 2,

x, y ≥ 0

Chapter: [0.12] Linear Programming

Show that the family of curves for which `dy/dx = (x^2+y^2)/(2x^2)` is given by x^{2} - y^{2} = cx

Chapter: [0.09] Differential Equations

Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`

Chapter: [0.07] Integrals

Solve the following equation for x: `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`

Chapter: [0.02] Inverse Trigonometric Functions

Using integration, find the area of region bounded by the triangle whose vertices are (–2, 1), (0, 4) and (2, 3).

Chapter: [0.08] Applications of the Integrals

Find the area bounded by the circle *x*^{2} + y^{2} = 16 and the line `sqrt3 y = x` in the first quadrant, using integration.

Chapter: [0.08] Applications of the Integrals

Find the equation of the plane through the line of intersection of `vecr*(2hati-3hatj + 4hatk) = 1`and `vecr*(veci - hatj) + 4 =0`and perpendicular to the plane `vecr*(2hati - hatj + hatk) + 8 = 0`. Hence find whether the plane thus obtained contains the line *x* − 1 = 2*y* − 4 = 3*z* − 12.

Chapter: [0.11] Three - Dimensional Geometry

Find the vector and Cartesian equations of a line passing through (1, 2, –4) and perpendicular to the two lines `(x - 8)/3 = (y + 19)/(-16) = (z - 10)/7` and `(x - 15)/3 = (y - 29)/8 = (z - 5)/(-5)`

Chapter: [0.11] Three - Dimensional Geometry

Consider f: `R_+ -> [-5, oo]` given by `f(x) = 9x^2 + 6x - 5`. Show that f is invertible with `f^(-1) (y) ((sqrt(y + 6)-1)/3)`

Hence Find

1) `f^(-1)(10)`

2) y if `f^(-1) (y) = 4/3`

where R_{+} is the set of all non-negative real numbers.

Chapter: [0.01] Relations and Functions

Discuss the commutativity and associativity of binary operation '*' defined on A = Q − {1} by the rule *a* * *b*= *a* − *b* + ab for all, a, b ∊ A. Also find the identity element of * in A and hence find the invertible elements of A.

Chapter: [0.01] Relations and Functions

If the sum of lengths of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is π/3.

Chapter: [0.06] Applications of Derivatives

if `A = ((2,3,1),(1,2,2),(-3,1,-1))`, Find `A^(-1)` and hence solve the system of equations 2x + y – 3z = 13, 3x + 2y + z = 4, x + 2y – z = 8

Chapter: [0.03] Matrices

Find the particular solution of the differential equation

`tan x * (dy)/(dx) = 2x tan x + x^2 - y`; `(tan x != 0)` given that y = 0 when `x = pi/2`

Chapter: [0.09] Differential Equations

#### Other Solutions

#### Submit Question Paper

Help us maintain new question papers on Shaalaa.com, so we can continue to help studentsonly jpg, png and pdf files

## CBSE previous year question papers Class 12 Mathematics with solutions 2016 - 2017

Previous year Question paper for CBSE Class 12 Maths-2017 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.

By referring the question paper Solutions for Mathematics, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of CBSE Class 12.

How CBSE Class 12 Question Paper solutions Help Students ?

• Question paper solutions for Mathematics will helps students to prepare for exam.

• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.

• For finding solution of question papers no need to refer so multiple sources like textbook or guides.